Friday, December 9, 2016

Let Them Make Mistakes

One of the pitfalls we find ourselves falling into as math teachers (I use the first person plural here because I have done this and I see others doing it too) is we facilitate our instruction with a goal that everyone gets it right.

It is easy to forget that the Everyday Math lessons we teach are structured in a way that allows and even encourages children to make mistakes.  In any lesson on any given day, we should expect students to make mistakes while they work, and especially when they think aloud.

Let's look at this in terms of the parts of a lesson.

Warm-up.

For the Warm-Up portion of Everyday Math lessons, Mental Math and Fluency is a check-in opportunity.  This is not a time to make sure all students get it; it is a time to check for mastery. That's why there are three levels of difficulty for the mental math segment of every lesson.  If most students appear to struggle with the first level, don't go onto the next.  Mental math is a chance for you to have a snapshot of your students' levels of math fluency before you get into the bulk of the lesson.  What you see in mental math might impact how you facilitate the rest of your lesson.  Mental Math is not the time to clear up misconceptions, or to keep providing more examples until everyone gets it right.  "What do you see?" when flashing a Quick Look card, or "How do you see that?" are great questions to ask that will elicit formative information.  But asking every student to share a strategy, or making sure every student gets it right will take too long and disengage students.

Mental Math.

Mental math is your students' opportunity to get their feet wet, so let them.  They might make mistakes.  Give them opportunities to make those mistakes, and then let them talk to each other about their mistakes.   The Teacher's Lesson Guide gives you a little suggested script to follow up after the Math Message. Notice it never says, Keep quizzing children until everyone gets it right.  Instead, it usually offers a differentiation strategy with suggestions for scaffolding.  Your scaffolds should not be "hints," but rather sentence structures to help them grasp a strategy, or visual aides to help them understand how to use a tool.  We still want to give them opportunities to figure out the problem for themselves (and to occasionally make mistakes, even with scaffolds).

Math Journal work.

They can make mistakes here too!  But now their mistakes are visible on paper.  The journal work is an excellent opportunity for students to work together, check each other's work, and compare strategies.  Two partners have different answers?  Wonderful!  Have them see if they can come to a consensus.  The "growth mindset" in math requires that students make mistakes, and do it fairly often.  Every time a student truly discovers the root of his or her mistake, that student has gained significant mathematical understanding.

Practice.

Mistakes are still encouraged here, while playing a game or working on math boxes. Here, mistakes are likely smaller and quickly resolved, but they still can and do happen.  This is where we want students to be able to catch and correct their own mistakes, either on their own or with the help of a partner.  If there are a lot of mistakes at this point of the lesson, that informs you that some extra practice or re-teaching may be necessary.

You may find that persistently allowing students to make mistakes actually saves you instruction time, because you are not so busy going from child to child making sure every student has gotten every part of the problem right, or demonstrated every strategy correctly.  Sometimes, that can postpone the entire class from proceeding to the next part of the lesson.  Instead, use those mistakes as learning opportunities, turn-and-talk topics, group consensus opportunities, and formative evaluation of their understanding for future instructional decisions.


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